This tutorial is for stock 2.1 Eclair Samsung Captivate only...
Download the latest version of the ROM. http://cognition.designgears.com/ Move it to your internal SD card on your phone.
If you are not already rooted, root by putting your phone in debug mode. Menu, settings, applications, development, USB debugging.
Download Samsung drivers for your system: http://forum.xda-developers.com/showthread.php?t=728929
Download the root file here: http://www.intomobile.com/2010/07/21/root-the-att-samsung-captivate-galaxy-s-tutorial/
Follow the instructions found in the above link and you are successfully rooted.
Disconnect phone from computer.
Next, download ROM Manager from the android market.
Choose "Flash Clockwork Mod" which will put an update.zip (holding clockwork recovery) on the root of your internal SD card.
Open Rom Manager, choose "Install ROM from SD Card", navigate to your Cognition2.x.zip, and watch the magic happen!
Notes:
If this is your first time installing clockwork, it may fail at stock recovery and reboot. Simply choose "reinstall packages" once more, and it should work properly.
You can then copy the update.zip to you comp and when you flash back to stock just copy that back over to the internal sd card and reboot to recovery and reinstall pkgs
Full instructions can be found here: http://cognition.theidiotshideout.net/mw/index.php?title=FAQ#Can_I_flash_this_over_my_current_ROM.3F
